SOM's mathematics

Authors:
J. C. Fort
Affiliations:
Laboratoire de Statistique et Probabilités, Toulouse, France
Venue:
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Year:
2006

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Abstract

Since the discovery of the SOM's by T. Kohonen, many results that provide a better description of their behaviour have been found. Most of them are very convincing, but from a mathematical point of view, only a few are actually proved. In this paper, we make a review of some results that are still to be proved and give some framework to formulate various questions.